I don't think American carriers are declining, I think foreign carriers are catching up.

Years ago, PanAm flew around the world (or close to it). You could fly anywhere with PanAm. Even later on, American carriers flew to many foreign destinations. If you wanted to fly to Australia or New Zealand not too long ago, United was your best bet.

But now, foreign carriers have upped their game. They are flying directly into the US, not only to JFK and LAX, but second-tier cities as well. For example, United quit flying to NZ after Air NZ came in. Most US carriers abandoned India after European (and later Middle Eastern) carriers increased frequency and started providing good connections. Americans are increasingly comfortable flying on foreign carriers. Rather than trying to serve the world, US carriers are now settling into their niche.

A similar thing happened with manufacturing. Once upon a time, Boeing virtually monopolized the large passenger aircraft market. Then Airbus came in and Boeing's share started falling. This doesn't represent the decline of Boeing, but rather then success of Airbus.